List of top Mathematics Questions asked in KEAM

If $sin\alpha +sin \beta = \frac{\sqrt6}2$ and $cos \alpha + cos\beta = \frac{\sqrt2}2$ then $coas(\alpha - \beta)$ is equa; to

The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0,-4) is

If ay=x+b is the equation of the line passing through the points (-5,-2) and (4, 7), then the value of 2a + b is equal to

$tan(2tan^{-1}(\frac{2}5))$ is equal to

The value of θ in the range 0 ≤ θ ≤ π/2 which satisfies the equation sin (θ + π/6) = cosθ is equal to

If cosecθ + cotθ = 5, then the value of tanθ is equal to

If 0 < θ < $\frac{π}2 $ and tanθ = $\frac{\sqrt5}2$, then cosθ is equal to

The value of $tan^{-1} (\frac{7}4) - tan^{-1} (\frac{3}{11})$ is equal to 

The value of $sin^2(cos^{-1}(\frac{3}5))$ is equal to

The set of all integer values of x that satisfy the inequality 19 ≤ 3x ≤ 27 is

Sum of last $30$ coefficients in the binomial expansion of $(1 + x)^{59}$ is

The sum of odd integers from $1$ to $2001$ is

Let $f : \bullet \to \bullet $ satisfy $f (x) f ( y) = f (xy) $ for all real numbers $x$ and $y$. If $f (2)= 4$, then $f \left( \frac{1}{2} \right) = $

The focus of the parabola $y^2 - 4y - x+3=0$ is

The focus of the parabola $( y + 1)^2 = -8(x +2)$ is

Eccentricity of the ellipse $4x^2 + y^2 -8x + 4y -8= 0$ is

Let $f (x) = px^2 + qx + r$ , where $p, q, r$ are constants and $p \neq 0$ . If $f (5) = -3 f (2)$ and $f (-4) = 0$ , then the other root of $f$ is

Which of the following is the equation of a hyperbola?

Three players A, B and C play a game. The probability that A, B and C will finish the game are respectively $\frac{1}{2} , \frac{1}{3}$ and $\frac{1}{4}$ . The probability that the game is finished is

$\lim_{x \to \infty} \frac{3x^3 + 2x^2 - 7x + 9 }{4x^3 + 9x - 2 }$ is equal to

The equation $5x^2 + y^2 + y = 8$ represents

The eccentricity of the ellipse $ \frac{\left(x-1\right)^{2}}{2} + \left(y + \frac{3}{4}\right)^{2} = \frac{1}{16}$ is

If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$

The equation of the tangent to the curve $y = x^3 - 6x + 5$ at $(2,1)$ is

If a and ??are the roots of 4x2 + 2x + 1 = 0, then ??=